Geodesic
Lagrangian mechanics and dry friction
Russian journal of nonlinear dynamics, Tome 6 (2010) no. 4, pp. 855-868.

Voir la notice de l'article provenant de la source Math-Net.Ru

A generalization of Amantons' law of dry friction for constrained Lagrangian systems is formulated. Under a change of generalized coordinates the components of the dry-friction force transform according to the covariant rule and the force itself satisfies the Painlevé condition. In particular, the pressure of the system on a constraint is independent of the anisotropic-friction tensor. Such an approach provides an insight into the Painlevé dry-friction paradoxes. As an example, the general formulas for the sliding friction force and torque and the rotation friction torque on a body contacting with a surface are obtained.
Keywords: Lagrangian system, Painlevé condition.
Mots-clés : anisotropic friction 
@article{ND_2010_6_4_a8,
     author = {V. V. Kozlov},
     title = {Lagrangian mechanics and dry friction},
     journal = {Russian journal of nonlinear dynamics},
     pages = {855--868},
     publisher = {mathdoc},
     volume = {6},
     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2010_6_4_a8/}
}
TY  - JOUR
AU  - V. V. Kozlov
TI  - Lagrangian mechanics and dry friction
JO  - Russian journal of nonlinear dynamics
PY  - 2010
SP  - 855
EP  - 868
VL  - 6
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ND_2010_6_4_a8/
LA  - ru
ID  - ND_2010_6_4_a8
ER  - 
%0 Journal Article
%A V. V. Kozlov
%T Lagrangian mechanics and dry friction
%J Russian journal of nonlinear dynamics
%D 2010
%P 855-868
%V 6
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ND_2010_6_4_a8/
%G ru
%F ND_2010_6_4_a8
V. V. Kozlov. Lagrangian mechanics and dry friction. Russian journal of nonlinear dynamics, Tome 6 (2010) no. 4, pp. 855-868. http://geodesic.mathdoc.fr/item/ND_2010_6_4_a8/

[1] Argatov I. I., Dmitriev N. N., Osnovy teorii uprugogo diskretnogo kontakta, Politekhnika, SPb., 2003, 233 pp.

[2] Zhuravlev V. F., “O modeli sukhogo treniya v zadache kacheniya tverdykh tel”, PMM, 62:5 (1998), 762–767 | MR

[3] Painlevé P., Leçons sur le frottement, Hermann, Paris, 1895; Penleve P., Lektsii o trenii, Gostekhizdat, M., 1954, 316 pp.

[4] Ivanov A. P., Osnovy teorii sistem s treniem, NITs «RKhD», IKI, M.–Izhevsk, 2011, 304 pp.

[5] Arnold V. I., Kozlov V. V., Neishtadt A. I., Matematicheskie aspekty klassicheskoi i nebesnoi mekhaniki, URSS, M., 2002, 414 pp.

[6] Kozlov V. V., Treschev D. V., Billiardy: Geneticheskoe vvedenie v dinamiku sistem s udarami, MGU, M., 1991, 168 pp.

[7] Vantorin V. D., “Dvizhenie po ploskosti s anizotropnym treniem”, Trenie i iznos v mashinakh, 16 (1962), 81–120

[8] Dmitriev N. N., “Nachalo dvizheniya tel po ploskosti s ortotropnym treniem”, Dinamika i ustoichivost mekhanicheskikh sistem, SPbGU, SPb., 1995, 14–20

[9] Markeev A. P., Dinamika tela, soprikasayuschegosya s tverdoi poverkhnostyu, Nauka, M., 1992, 336 pp.

[10] Sommerfeld A., Vorlesungen über theoretische Physik, v. 1, Mechanik, 2. Aufl., Akad. Verl., Leipzig, 1944; Zommerfeld A., Mekhanika, IL, M., 1947, 391 pp.

[11] Karapetyan A. V., “O modelirovanii sil treniya v dinamike shara na ploskosti”, PMM, 74:4 (2010), 531–535